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February 8th, 2013, 07:41 PM  #1 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,545 Thanks: 924 Math Focus: Elementary mathematics and beyond  Book on elementary number theory
Any recommendations for a good book on elementary number theory, preferably something that lays a solid foundation for continuing study in the field?

February 8th, 2013, 07:48 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 462 Math Focus: Calculus/ODEs  Re: Book on elementary number theory
I have (but have not studied yet...but someday! ) "An Introduction to the Theory of Numbers" by G.H. Hardy and E.M. Wright, Fifth Edition. I have seen it highly recommended by others both for accessibility and coverage.

February 8th, 2013, 10:15 PM  #3  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Book on elementary number theory Quote:
Try Crandall & Pomerance if you want to get an introduction to computational number theory and some analytical number theory.  
February 12th, 2013, 06:45 AM  #4 
Senior Member Joined: Aug 2010 Posts: 195 Thanks: 5  Re: Book on elementary number theory
Hardy and Wright's book is certainly a quality text, but it memory serves, it lacks exercises and is an older book. If you actually want to learn number theory, you need to do a lot of problems. You might consider Silverman's Friendly Introduction to Number Theory (the third edition is particularly inexpensive now that the fourth is out), it can be a bit fluffy, but it tries to guide readers through figuring things out on their own. It also has a bit more of an algebraic and geometric flavor. Ultimately, I think it is useful to "graduate" to more advanced books as quickly as possible. Much of the truly excellent exposition on number theory is written at the beginning graduate level. I recommend getting copies of: Apostol Introduction to Analytic Number Theory Ireland and Rosen A Classical Introduction to Modern Number Theory even if only to decorate your shelves for a little while. Apostol's book is actually fairly elementary and only really requires some fairly basic analysis. Ireland and Rosen steadily assume more and more abstract algebra but start out fairly modest (you should know what a principle ideal domain is before starting this book), but is easily my favorite nonexpert book on number theory. In the end, you should probably also get a copy of Hardy and Wright's book, as it is an excellent reference, especially when starting out. 
February 12th, 2013, 07:31 AM  #5  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Book on elementary number theory Quote:
Quote:
 
January 17th, 2014, 11:54 PM  #6 
Newbie Joined: Oct 2013 From: Bangladesh Posts: 4 Thanks: 0 Math Focus: Number Theory, Combinatorics  Re: Book on elementary number theory
If you 'really' want to study number theory, you need a theory book and also a book with a lot of challenging problems. Among theory books, I think 'Elementary Number Theory' (fifth edition) by David Burton is the best available online. As a problem book, I would highly recommend both of '104 number theory problems' and 'Number Theory: Structure, examples and problems' by Titu Andresscu These two books are Olympiad oriented and can really give you a greater insight into the beauty of number theory.

January 20th, 2014, 06:41 PM  #7 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Book on elementary number theory
Ireland & Rosen is what I learned number theory from, but I don't recommend it for beginners. It's better for a second course in (algebraic) number theory. Similarly, I find Apostol too advanced. In a pinch you could start with Hardy & Wright but you won't get far if you lack other experience. The other suggestions are probably more appropriate. 
January 20th, 2014, 11:15 PM  #8 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Book on elementary number theory
I am trying Iwaniec & Kowalski now, do you think it's good for me?

January 21st, 2014, 07:46 AM  #9  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Book on elementary number theory Quote:
 
January 21st, 2014, 07:52 AM  #10 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Book on elementary number theory
I see. What did you use for combinatorial number theory then?


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